A chord is drawn through the focus of the parabola $\;y^{2}=6x\;$ such that its distance from the vertex of this parabola is $\;\large\frac{\sqrt{5}}{2}\;$ , then its slope can be :

Question

$(a)\;\large\frac{\sqrt{5}}{2}\qquad(b)\;\large\frac{\sqrt{3}}{2}\qquad(c)\;\large\frac{2}{\sqrt{5}}\qquad(d)\;\large\frac{2}{\sqrt{3}}$